The
Holy Grail for many of today's theoretical physicists is a complete
quantum mechanical theory of gravity -- useful for understanding the
behavior of black holes, big bangs, and whole universes. But bridging
the gap between the smallest and largest constituents of reality will
probably require a few totally new concepts (and shake our faith in
some old ones). One researcher looking for these missing pieces is
Raphael Bousso of Harvard University. The 31-year-old shared first
prize in an international competition for young physicists last year
for his work on the so-called holographic principle, which aims to
reconcile quantum mechanics with black hole physics. His research has
led him to think hard about string theory and cosmology, too.

Scientific
American [SA]: String theory tells us that particles are these tiny
loops or squiggles all tangled together. What has string theory done
that we should believe any of that?

Raphael
Bousso [RB]: String theory offers a framework in which all forces are
naturally, completely unified, including gravity. We really don't have
anything else that achieves the same kind of unification. If you ask
what string theory has done, for example, it describes in principle how
the particles that make up gravity interact with each other. And it has
explained in certain very special cases the entropy of black holes,
which is a big problem in quantum gravity.

SA:
In the past few years string theorists have started thinking about
cosmology, in particular this dark energy that seems to be making
galaxies spread apart faster over time. What's the fascination?

RB:
We don't really know what this stuff is. There are a lot of different
possibilities for types of matter that will act the way that this dark
energy seems to be acting on our universe. From a theorist's standpoint
they are very different things. An example of that distinction is
whether that dark energy is really what we call a cosmological
constant, in which case its density is fixed and will never change. Or
if it is something that acts for a while like a cosmological constant,
accelerating the universe, but eventually gets diluted. That's
something that we currently can't distinguish very well with the
experimental evidence, but it has an enormous effect on the large-scale
structure of the universe and what the world will look like in the far
future. It would be very nice to understand what kinds of dark energy
are favored from a theoretical perspective. The biggest question is,
why is it there at all? And we really have a hard time understanding
that because it's so incredibly small yet it isn't zero. That poses a
huge challenge for theory to explain.

RB:
There is a tension there. What most people would agree on is that it's
very likely that the explanation of the origin of the cosmological
constant will come from a quantum theory of gravity. That wouldn't have
to be string theory. But string theory is the best, most accurate and
most powerful candidate theory that we have. Now the tension comes from
the fact that it's been very difficult to find cosmological solutions,
in particular solutions with positive dark energy, in string theory.
[In general relativity, the cosmological constant could be positive and
repulsive or negative and attractive.] While string theory's our best
candidate for quantum gravity, we're a little disappointed by the fact
that so far we've not managed to model universes with dark energy in
string theory.

SA: What makes the problem difficult?

RB:
There is a problem in universes with a positive cosmological constant.
Now this problem doesn't occur for all types of dark energy, but for a
certain class of universes that exhibit dark energy you cannot measure
the [end] state [of particle interactions], because particles get
causally separated. There's no one who can see them all. In that sense
you cannot measure the result of any scattering [of particles].
Experiments in high-energy physics are best described by the formalism
called the S-matrix, which gives you the probability, for all the
different things that you put in, of all the different things that
could come out. That formalism comes from the days when we thought that
all of the world of physics is particle accelerators, where we're
playing "God" [more literally, an observer at the edge of spacetime]
sitting on the outside sending some particles in -- say an electron and
a positron or something -- crashing them together with great force and
looking at what comes out.

This
thing that describes the relation between what you shoot in from far
away and what comes back out from that interaction region, when the
particles are again well separated and detected in your detector, that
thing is the S-matrix. Because we were doing physics at a very small
scale, that language was a useful language to describe the world.
String theory, which historically is rooted in particle physics, likes
to predict an S-matrix and not much else. But clearly that language
can't be right to describe an experiment in cosmology, where we don't
have any control over what "God" sent in. We're just looking through
our telescope and seeing some stuff that hits us. So the difference
between cosmology and the S-matrix is that in the S-matrix you're
outside looking in and in cosmology we're inside looking out.

SA: Is this a problem only for universes with dark energy?

RB:
You might have already been very suspicious, dark energy or not, of the
idea that an S-matrix could describe experiments in cosmology. What
people have sharpened lately is the statement that you simply cannot
even define an S-matrix in many cosmological space times, in particular
some in which there is dark energy. The reason for that is that to
define an S-matrix, you have to be able to look at what comes out of an
experiment at arbitrarily large distance scales. You have to let
particles get far, far away from each other so that they stop
interacting and you can really say, this is what came out and not
something else. If the universe accelerates too fast, it's not possible
for a single observer to see all the particles that come out. Some of
them disappear behind what's called an event horizon. I can't look at
them and then bring the information back to me, the spacetime in
between me and the particles is accelerating too fast. So that poses a
challenge in the sense that we simply don't know what replaces the
S-matrix as the correct "observable." We don't know what the right
question is that we want our theory to answer in such cosmologies. If
it turns out that we can describe dark energy in string theory in some
model, then we would expect that string theory is going to tell us,
what are the observables, what are the questions we can ask in that
model?

SA: Could string theory ever be up to this challenge?

RB:
What we should focus on is the question of whether or not string theory
is currently developed enough to understand cosmology and dark energy,
or whether there are some important bits that we're still missing. If
you look at history, what we call string theory today is a vastly
richer structure than what we called string theory 10 years ago [when
physicists couldn't use it to calculate the entropy of a black hole].
It seems to me there's a real possibility that trying to use string
theory as we see it today to explain the cosmological constant problem
is like trying to use the 10-years-ago string theory to explain black
hole entropy. Maybe we're not quite there yet, maybe we need to make
some conceptual progress in the theory before we can do that. So my own
interest is in trying to get some hints of what kind of things we might
be missing, in which directions do we need to explore.

SA: What kind of hints have you and others seen?

RB:
The hints that we are getting are similar to the kind of hints we've
been getting from semi-classical [not fully quantum mechanical] physics
about black holes. Semi-classical analyses told us that black holes
have an entropy, though it didn't tell us where that entropy comes from
microscopically. [The entropy of a glass of water comes from the many
possible equivalent arrangements of the molecules within.]

In
the case of universes with a positive cosmological constant,
semi-classical physics, and in particular an idea called the
holographic principle [which holds that the maximum entropy of a region
of spacetime is proportional to its area, as opposed to its volume], is
telling us that those universes have a finite entropy. In other words,
you simply cannot put a black hole, which is the densest, most entropic
object you can imagine, beyond a certain size into a universe with
positive cosmological constant. No experiment that you make in such a
universe will ever see more entropy than about the inverse [of the
value of the] cosmological constant. As the dark energy goes to zero,
that statement goes away.

What
we're finding is this pattern where the presence of dark energy -- it
has to be a fixed cosmological constant to really make this statement
-- seems to correspond to theories with a finite entropy. These
[finite-entropy theories] are things that haven't really popped up yet
in string theory or, for that matter, anywhere else. And that's the
kind of statement that might be a very useful hint as to which
direction we should be looking in.